An initial investment of $200 is worth $315.24 after seven years of continuous compounding. Find the interest rate.​

Answer: A.26

Step-by-step explanation:

= 3f+g

= 3 (6)+8

=26

Answer:

a. 3

Step-by-step explanation:

[tex]6 {x}^{2} - 3x + 18 \\ \\ = 3(2 {x}^{2} - x + 6) \\ \\ GCF = 3[/tex]

the greatest common factor of 6x2 – 3x + 18 is 3.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life

Here, given that,

6x2 – 3x + 18

=3×(2x2-x+6)

Hence, the greatest common factor of 6x2 – 3x + 18 is 3.

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Answer:

h<=4

Step-by-step explanation:

-9h+3<=-7h-5

-9h+7h<=-5-3

-2h<=-8

h<=4

Answer:

5.625 pounds or 5 5/8 pounds

Step-by-step explanation:

(2 1/4)/24 = weight of one golf ball = 0.09375

0.09375 x 60 = 5.625 pounds or 5 5/8 pounds

Answer:

5.625 pounds or 5 5/8 pounds as a fraction

Step-by-step explanation:

Answer:

3w² = 243

Step-by-step explanation:

Width = w

Length = 3w

Area = 243 square units

length *width = 243

3w * w = 243

3w² = 243

The equation that you can used to determine the width of the rectangle with the given area is: 3w² = 243

Area = (length)(width)

The given dimensions are:

The equation to se in finding the width (w) of the rectangle will be:

3w(w) = 243

3w² = 243

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Answer:

area = 92 yd²

Step-by-step explanation:

13x8 = 104

3x8x0.5 = 12

104 - 12 = 92 yd²

Answer:

Step-by-step explanation:

Answer:

21

Step-by-step explanation:

Answer:

jajjajajja eres bien menos

Answer:

The difference is -2x10 is basically-2 times x times 10.

Step-by-step explanation:

Cuz i said so

The x values that makes the given inequality true are -10, -9, -8, -7 and -6.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

The given inequality is -2x>10.

Divide -2 on both the sides of an inequality, we get

x<-5

So, the solution is {.......-10, -9, -8, -7, -6}

Hence, the x values that makes the given inequality true are -10, -9, -8, -7 and -6.

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Answer:

5 < 8

-4 < 0

0 < 4

-5 < 5

-9 > -19

-5 > -8

Step-by-step explanation:

Remember, the "Alligator" or better known as the "Packman" symbol (  >  <  )

It will always want to "eat" the bigger number. so, 8 is bigger than five, so the "Packman" will want to go after the bigger number. 5 < 8

Answer:

464m^2

Step-by-step explanation:

Given data

Dimension of the regular playground

Length= 28m

Width= 15 m

We want to extend both sides by 1 m

Length= 28+1= 29m

Width= 15+1= 16m

Hence the area

Area=Length*Width

Area= 29*16

Area= 464m^2

The Area is 464m^2

I assume the _ characters are supposed to be minus signs, as in

3x ² + 3y ² - 7x - 6y - 3 = 0

Move the 3 to the right sides, and complete the square in x and y :

(3x ² - 7x) + (3y ² - 6y ) = 3

3 (x ² - 7/3 x) + 3 (y ² - 2y ) = 3

x ² - 7/3 x + y ² - 2y = 1

(x ² - 7/3 x + 49/36) + (y ² - 2y + 1) = 1 + 49/36 + 1

(x - 7/6)² + (y - 1)² = 121/36

(x - 7/6)² + (y - 1)² = (11/6)²

The circle thus has radius 11/6, so its diameter is 2 • 11/6 = 11/3.

Answer:

Step-by-step explanation:

I believe it is b

Answer:

https://brainly.com/question/22433896?answering=true&answeringSource=feedPublic%2FhomePage%2F1

Step-by-step explanation

Answer: click point (-4,4)

Step-by-step explanation:

here is the answer for the x and y axis

when in brackets x always comes first and y second

in this case x is -4 and y is 4

x axis goes like this----

y axis goes like this |

Answer :

Given : A and B are complementary angles. B and C are complementary angles.

Prove : A C

I have attached a picture of me doing it. Hope this helps, thank you :) !!

Answer:

As per above two statements we have:

and

Answer:

y=58×2=116 central angle of the cyclic quadrilateral is double if inscribed angle

z=90/2=45

inscribed angle is half of central angle of the cyclic quadrilateral

Answer:

1/8

Step-by-step explanation:

plz brainliest

Answer: x>1/2y+5/2 look at the picture it going to be the graph

Step-by-step explanation: Hope this help :)

Answer:

X=9

Step-by-step explanation:

I know this because you can find the answer by doing 28 - 10 which equals 18 and 2 times 9 gets you 18 and would make the equation

( 2 times 9) + 10= 28

18 + 10=28

Answer:

C, f(x) = 3(2)^x

Step-by-step explanation:

Since the y-intercept is 3, the function will have 3 multiplying by some number to the power of x.

As x increases by 1, we notice that y multiplies by 2 every time.

This leads us to believe that the equation is 3 * 2^x

The exponential function represented by the graph is:

[tex]f(x) = 3(2)^x[/tex]

It is modeled by:

[tex]y = ab^x[/tex]

In which:

In the graph, there is point (0,3), hence a = 3, and it also has point (1,6), hence:

[tex]6 = 3b[/tex]

[tex]b = 2[/tex]

Thus, the equation is:

[tex]f(x) = 3(2)^x[/tex]

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Answer:

(a) The equation for the number of bacteria at time t ≥ 0 is [tex]y = 200\cdot e^{0.5 \cdot t }[/tex]

(b) The average population in the bacteria for 0 ≤ t ≤ 10 is 29,482 bacteria

(c)  The growth rate of the bacteria in the first 10 hours is 14,841 Bacteria/hour

Step-by-step explanation:

(a) The given rate of growth of the bacteria population is;

[tex]\dfrac{dy}{dt} = 0.5 \cdot y[/tex]

The initial amount of bacteria = 200

At time, t ≥ 0, we have;

[tex]\dfrac{dy}{y} = 0.5 \cdot dt[/tex]

[tex]\int\limits {\dfrac{dy}{y} } = \int\limits {0.5} \, dt[/tex]

ln(y) = 0.5·t + C

[tex]y = e^{0.5 \cdot t + C}[/tex]

[tex]y = C_1 \cdot e^{0.5 \cdot t }[/tex]

When, t = 0, y = 200, we have;

[tex]200 = C_1 \cdot e^{0.5 \times 0 } = C_1[/tex]

C₁ = 200

The equation for the number of bacteria at time t ≥ 0 is therefore given as follows;

[tex]y = 200\cdot e^{0.5 \cdot t }[/tex]

(b) The expression for the average number of bacteria in the population for 0 ≤ t ≤ 10 is given as follows;

[tex]y = \int\limits^t_0 {0.5 \cdot y} \, dt[/tex]

[tex]y = \int\limits^{10}_0 {0.5 \cdot 200\cdot e^{0.5 \cdot t }} \, dt = \left[200\cdot e^{0.5 \cdot t }\right]^{10}_0 \approx 2,9682.6 - 200 = 29,482.6[/tex]

The average population in the bacteria for 0 ≤ t ≤ 10 is therefore, y = 29,482

(c)  The average rate of growth after 10 hours of growth is given as follows;

[tex]\dfrac{dy}{dt} = 0.5 \cdot y[/tex]

[tex]\dfrac{dy}{dt} = 0.5 \cdot 200\cdot e^{0.5 \cdot 10 } = 14,841.32 \ Bacteria/hour[/tex]

The growth rate of the bacteria in the first 10 hours is 14,841 Bacteria/hour

Population functions can either represent growth or decays.

The given parameter is:

[tex]\frac{dy}{dt}= 0.5y[/tex]

(a) Solve for y

We have:

[tex]\frac{dy}{dt}= 0.5y[/tex]

Integrate both sides

[tex]\int \frac{dy}{dt}= \int 0.5y[/tex]

Divide both sides by y, and multiply both sides by dt

[tex]\int \frac{dy}{y}= \int 0.5\ dt[/tex]

Integrate both sides of the equation

[tex]\ln(y) = 0.5t +c[/tex]

Take the exponent of both sides

[tex]y = e^{0.5t +c}[/tex]

This gives

[tex]y = ce^{0.5t}[/tex]

When t = 0, and y = 200.

So, we have:

[tex]200 = ce^{0.5 \times 0}[/tex]

[tex]200 = ce^{0}[/tex]

Evaluate the exponent

[tex]200 = c[/tex]

Rewrite as:

[tex]c = 200[/tex]

Substitute 200 for c in [tex]y = ce^{0.5t}[/tex]

[tex]y = 200e^{0.5t}[/tex]

Hence, the equation for y is [tex]y = 200e^{0.5t}[/tex]

(b) The average number of bacterial for 0 ≤ t ≤ 10.

The average value of the function is calculated as:

[tex]y' = y(10) - y(0)[/tex]

Calculate y(0) and y(10)

[tex]y = 200e^{0.5t}[/tex]

[tex]y(0) = 200e^{0.5(0)}= 200[/tex]

[tex]y(10) = 200e^{0.5\times 10} =29682.6318205[/tex]

So, we have

[tex]y' = y(10) - y(0)[/tex]

[tex]y' = 29682.6318205 - 200[/tex]

[tex]y' = 29482.6318205}[/tex]

[tex]y' = 29483[/tex]

Hence, The average number of bacterial for 0 ≤ t ≤ 10 is 29483

(c) The average rate over the first 10 hours of growth

We have:

[tex]\frac{dy}{dt}= 0.5y[/tex]

Substitute [tex]y = 200e^{0.5t}[/tex]

[tex]\frac{dy}{dt}= 0.5 \times 200e^{0.5t}[/tex]

[tex]\frac{dy}{dt}= 100e^{0.5t}[/tex]

When t = 10, we have:

[tex]\frac{dy}{dt}= 100e^{0.5 \times 10}[/tex]

[tex]\frac{dy}{dt}= 100e^{5}[/tex]

[tex]\frac{dy}{dt}= 14841[/tex]

Hence, the average rate over the first 10 hours of growth is 14841

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Answer:

associative property

Step-by-step explanation:

This is the associative property. The numbers and signs on both sides of the equation stay IN THE SAME ORDER, this is a big hint!

Answer:

associative property

Step-by-step explanation:

Answer:

Answer is A! 38 degrees

Step-by-step explanation:

opposite side is the same

Answer:

2.4 is the correct answer

Answer:

Pythagorean Theorem:

a^2 + b^2 = c^2

30^2 + b^2 = 35^2

b^2 = 325

b=18.03

Let me know if this helps!

Answer:

x = -3/2 or -1.5

Step-by-step explanation:

Answer:

Step-by-step explanation:

if C is the right angle,

AB is the hypotenuse

AB^2=AC^2+BC^2

AC^2=13^2-5^2

AC^2=169-25=144

AC=[tex]\sqrt{144}[/tex]=12

AC=12